Mare Chronium

A Brief History of Martian Time
1880-1999

An expanded and updated version of a paper presented at
the Case for Mars IV Conference, University of Colorado, Boulder, Colorado, USA
4 - 8 June 1990

Copyright © 1990, 1997-1999 by Thomas Gangale

Part 2

Robert A. Heinlein's 1949 novel Red Planet contained a brief reference concerning a Martian calendar. In the course of a conversation in Chapter 1:

Jim thought back over the twenty-four months of the Martian year. "Since along toward the end of Zeus, nearly November."

"And now here it is the last of March, almost Ceres, and the summer gone."

From this it is clear that Heinlein's calendar comprised the twelve Roman months of the Gregorian calendar, and with these were alternated twelve new months whose names were taken from Greek and Roman mythology. The fact that Heinlein's characters were living in the northern hemisphere of Mars also indicates that on his calendar, March occurred at the end of the northern hemisphere's summer, and therefore simultaneously at the end of the southern hemisphere's winter. As with Lowell's system, this is the opposite orientation to the Gregorian calendar on Earth. Other passages in the book refer to sols of the week with their familiar terrestrial names, implying that Heinlein's Martian calendar also incorporated the conventional seven-sol week.

Alfred Bester won the Hugo Award for The Demolished Man. While the novel is set in 2301 A.D. New York City and has nothing to do with Mars, in the first chapter the protagonist glances at a clock giving "the time panorama of the solar system." The dials read "February 15, 0205 Greenwich" for Earth and "Duodecember 35, 2220 Central Syrtis" for Mars.

Ray Bradbury used the Gregorian calendar for his chronology in The Martian Chronicles, and spoke of August 1999 as being summer on Mars, which it will indeed be in the northern hemisphere. However, Bradbury also had the following spring as occurring in April 2000, when in factit will still be the dead of winter in the northern hemisphere and the height of summer in the southern hemisphere. From this it appears that Bradbury mistakenly synchronized the Martian seasons with the seasons of Earth.

Arthur C. Clarke made a passing reference near the end of Chapter 8 of The Sands of Mars which definitely implies a twelve-month Martian calendar incorporating seven-sol weeks:

Gibson had not yet mastered the intricacies of the Martian calendar, but he knew that the week-days were the same as on Earth and that Monday followed Sunday in the usual way. (The months also had the same names, but were fifty to sixty days in length.)

For quite a long time, the fact that Clarke's months varied between fifty and sixty sols puzzled me. The few writers on the subject of Martian timekeeping that I had discovered at this point, as well as, had devised their calendars such that, if they had months in them, they were of even length. Why weren't Clarke's as well? Eventually it occurred to me that Clarke might have meant his months to represent the passage of Mars through equal arcs of thirty degrees in its elliptical orbit around the Sun. I made some calculations to check this idea and found that near perihelion Mars passes through a thirty degree arc in 46 sols, while near aphelion such an angle requires 67 sols. A variation on this idea would be to have the Martian months correspond to the passage of that planet through the same heliocentric longitude (relative to the Martian vernal equinox) as Earth does during the same months, in effect unevenly stretching the Gregorian calendar to fit the larger and more eccentric orbit of Mars. Clarke's comments seemed to make a rough cut at this idea without bogging his readers down in details. It is a curious coincidence that just as I hit upon this idea, Makoto Nagatomo was writing a letter to the British Interplanetary Society in response to my July 1988 Spaceflight article "The Lost Calendars of Mars". As I was to shortly discover, and as I will later discuss in this paper, the months on Nagatomo's calendar are indeed based on stretching the Gregorian calendar, and in retrospect, it is possible that Heinlein's were as well. Nagatomo's correspondence was followed a month later by a letter from George E. Henry, who it turned out had also devised a Martian calendar based on the same idea. Recently, Frank Bauregger developed yet another "stretched Gregorian" calendar. So far as I know, the Zubrin calendar is the only example of an equal-arc calendar.

While searching for the details of what at the time I believed to be Richardson's calendar (but was actually Aitken's), I discovered evidence of yet another lost Martian calendar -- and the first construction of a Martian clock -- invented by his contemporary I. M. Levitt. I also subsequently found that in addition to describing the Aitken calendar, Richardson mentioned the Martian calendar devised by Levitt in a footnote of Exploring Mars.

Levitt published his idea of a Martian calendar in the May 1954 issue of Sky & Telescope and later in Appendix 1 of his 1956 book, A Space Traveller's Guide to Mars. He devised yet a different method of intercalation from those discussed by Richardson and the one adopted by Aitken. He specified a five-year sequence in which the first and fourth years were 668 sols long and the other three years contained 669 sols. Additionally, however, Levitt allowed for the omission of a leap sol every 1,000 years and therefore claimed for his calendar an accuracy of one sol in 20,000 years.

Despite the fact that the lunar cycle, the natural basis for the month as a unit of time, has nothing at all to do with Mars, Levitt saw that the month was nevertheless a very desirable unit of time to transplant to Mars. However, instead of having the Martian months approximate the lunar cycle (about 29 Martian solar days) and thus having more months in the longer Martian year, Levitt proceeded along a different line of reasoning and instead divided the Martian year into twelve months, as do most calendars on Earth.

Levitt's months are thus nearly twice as long as the months on the Gregorian calendar, averaging just slightly less than 56 sols each.

Of all the Martian solar calendars ever devised, Levitt's is one of the most conservative. He retained the same names of the twelve months of the year that date back to ancient Rome. The Levitt calendar inherited the seven-day week from the Gregorian calendar, and also preserved the Anglicized names of the seven days of the week. There is on his calendar, however, an interesting departure from the convention of the Gregorian calendar which makes it superior to the Gregorian calendar and also gives it a definite advantage over the Aitken calendar. As with Aitken's calendar, Levitt's divides the Martian year into equal quarters of 167 sols, except in the case of the last quarter of a 669-sol year, which is 168 sols. But as opposed to Aitken, who employed unvarying seven-sol weeks throughout his calendar so that the sols of the week slid backward from quarter to quarter, Levitt contrived a six-sol week to end each 167-sol quarter. Levitt's six-sol weeks end with Friday and are immediately followed by Sunday. As a result, every month on the Levitt calendar begins with a Sunday, the first sol of the week, and thus his calendar is perpetual over a 56-sol period (refer to the table). Any given sol of the week can only occur on precisely eight dates of the month; "If it's Tuesday, this must be the 3rd, or the 10th, or the 17th, et cetera." This would be as easy to memorize as multiplication tables.

While Aitken did not designate a beginning year for his calendar, Levitt did, and thus his calendar can be correlated to Earth's Gregorian calendar. In the absence of any Martian historicalevent on which to base a Martian calendar, Levitt tied the beginning of his Martian chronology to the beginning of the Julian Period. Levitt began his Martian chronology with the year 0 rather than 1. Thus 1 January 4713 B.C. on the Julian calendar was also 1 January 0 M.Y. (Martian Year) on the Levitt calendar. Although Levitt did not furnish an exact correlation between his calendar and a modern date on the Gregorian calendar in his May 1954 Sky & Telescope article, he did state that 1 January 1954 A.D. occurred in the year 3641 M.Y.

Levitt also considered the problem of reducing the Martian sol into smaller units of time. His idea was a simple one, and it has been duplicated many times since by other writers. Levitt divided the sol into 24 hours, and these were further broken down into units of 60 minutes with each minute in turn containing 60 seconds, just as we do on Earth. Of course, since the Martian solar day is 2.7 percent longer than the terrestrial solar day, each of these Martian units of time are proportionately longer in duration. This difference is so slight that, without actually comparing two chronometers each calibrated to the timekeeping system of the respective planet, one would indeed be hard pressed to notice the difference (if a Martian tells you that he'll be there in a minute, are you really going to notice if he slows up about three seconds late?).

Levitt turned his ideas on Martian timekeeping into actual hardware, thereby creating the first operational system of Martian time. Designed by Levitt and constructed in the home workshop of Ralph B. Mentzer of the Hamilton Watch Company, the Earth-Mars clock was unveiled at the Waldorf-Astoria Hotel in New York on 14 February 1954. The main dial of the clock displayed the time of "sol" on Mars; whether or not this was intended to be Martian Prime Meridian Time is unclear. Additionally, the clock had three smaller dials on its face: the first marked the sol, month, and year on Mars according to the Levitt calendar; the second displayed 24-hour Greenwich Mean Time; the third showed the day, month, and year according to the Gregorian calendar. The Levitt-Mentzer clock was capable of being run forward or backward at 2,000 times normal speed and stopped at any date between 1 January 1970 and 31 December 1989, and thus functioned as a mechanical analog computer for relating time on both worlds. Recall that at the time Levittand Mentzer devised their clock, electronic digital computers were cumbersome, expensive, and still quite rare.

An HTML version of Levitt's article, "Mars Clock and Calendar", and of the 15 February 1954 New York Times story, "Mars Clock in Debut", are available on the Martian Time Web Site.

Carl Jacobi's short story "The Martian Calendar" revolves around a mysterious Martian mechanism which not only measures the passage of time, but apparently alters it as well. However, the story describes only one detail of the Martian timekeeping system, and it is dead wrong. Unfortunately, Jacobi was under the mistaken impression that the Martian year lasts 687 Martian sols, thereby repeating the error that Burroughs committed nearly half a century before.

When Terran archaeologists identify a periodic table in the ruins of an ancient Martian university in H. Beam Piper's "Omnilingual", it serves as a Martian Rosetta Stone, allowing Terrans to transliterate a portion of the Martian language for the first time. In the course of this absorbing tale the archaeologists learn that the Martians divided their "masthar" (year) into ten more or less equal "mastharnorvod" (months). It is disclosed that the name of each month is simply the number of its order in the calendar year, which calls to mind the Roman calendar's Quinctilis (later Julius), Sextilis (later Augustus), Septembris, Octobris, Novembris, and Decembris. The names of only six of these Martian months are given: Trav (first), Sanv (second), Krav (third), Doma, fifth), Yenth (eighth), and Nor (tenth).

Weeks were not mentioned in Piper's story, but since one may presume that each month contained either 66 or 67 sols, the division of each month into eleven six-sol weeks would be a logical development. One can also speculate that, rather than having each month begin haphazardly on any sol of the week as the Gregorian calendar does, the Martians might have taken advantage of the nearly perfect division of each month by six, thus choosing instead to treat the 67th sol of the month as an intercalary sol and allowing each month to begin on the first sol of the week (refer to the table). Of course, this is only speculation, but it does illustrate that a six-sol week could work quite well on Mars.

In Chapter 1 of D. G. Compton's Farewell Earth's Bliss, one of the transportees to the penal colony on Mars passed the time on the voyage by speculating on the structure of the Martian calendar:

Fifty-seven days hath September,
April, June, and November.
All the rest have fifty-eight,
Save poor February's fate,
Having fifty-three days clear,
And fifty-two in each Leap Year.

Nobody on board had any real idea how the people in the settlement would have organised their six-hundred-and-eighty-seven-day year.

Evidently! Once the new convicts reached Mars, they should have discovered that the Martian year was really only 668 sols. By the end of the novel, most of them had run out of time anyway.

Up until now, all of the calendars I have discussed that were developed beyond mere passing references from novels or short stories have been constructed on equal divisions of the Martian year. On the other hand, the Clarke calendar, with its months varying between fifty and sixty sols, seems to have been based instead on months corresponding to the movement of Mars through roughly the same arcs as their counterparts on Earth, or approximately thirty degrees. The 24-month Heinlein calendar may also have embodied this concept (fifteen-degree arcs in this case), since the summer was gone at the end of March and therefore the autumnal equinox would presumably occur in early Ceres (the sixth month), and one can further surmise that the winter solstice, vernal equinox, and summer solstice would fall early in the twelfth, eighteenth, and twenty-fourth months, respectively.

George E. Henry, writing in his regularly appearing column in the Daytona Beach Morning Journal, approached the subject of a Martian calendar from this same direction. Starting with twelve months as did Clarke, and choosing a northern hemisphere bias as opposed to Heinlein's southern bias, Henry essentially stretched the Gregorian calendar to fit the Martian year so that the vernal equinox, the summer solstice, autumnal equinox, and winter solstice would take place in late March, June, September, and December, respectively, just as they do on Earth. His calendar perpetuates the flaws of the terrestrial model on which it is based. The months begin haphazardly on varying days of the week, as do the years, and thus it is not perpetual. He even kept the leap-sol at the end of February, instead of placing it at the end of the year where it would make more sense. After all, February was originally made the month of variable length when it was the last month of the Roman calendar rather than the second (at that time, September was the seventh month, as its name implies!).

Since Henry had to write his newspaper column to a tight space constraint and to a general audience (which of course had to be given a quick lesson in the pertinent astronomical concepts within that tiny space), his description of a Martian calendar was necessarily brief and lacking in detail. He did touch on the subject of intercalation, noting that six out of every ten years must be a leap year, but did not specify a sequence for these. There was no correlation given for a specific date on his calendar and a corresponding Gregorian date.

The first practical need for a Martian calendar of even a rudimentary form, and for a system of time based on Martian solar days rather than terrestrial solar days, began with the landing of the Viking 1 spacecraft, when project members began expressing Martian solar days as "sols". The sol of the landing, 20 July 1976, they designated "Sol 0", and the sols that followed were numbered successively. With the landing of this first unmanned spacecraft, humans began working on the surface of Mars, albeit by proxy. Thus it was that humans began working by Martian time, working their daily schedules around the daylight hours at the two Viking lander sites. This was the true beginning of Martian chronology, for although the Levitt-Mentzer clock was constructed more than two decades earlier, it was apparently never used as much more than a planetarium exhibit.

The Viking invasion of Mars inspired an invasion of the bookstands by a host of books about Mars. One of them was Patrick Moore's 1977 revision of Guide to Mars, and in it was a description of yet another Martian calendar. Moore's idea was to divide the Martian year into 18 months, all but three of which would be 37 sols long. The 6th, 12th, and 18th months were instead 38 sols long. Moore made no mention of weeks in his calendar, and indeed, since 37 is a prime number, there is no hope of having an integral number of weeks -- seven-sol weeks or otherwise -- in his months, as Levitt had in his calendar. Neither could the Moore calendar approach the equally elegant solution of the Aitken calendar's two-year cycle. Yet the sociological need for the week as a unit of time is incontrovertible, and certainly the Martians will not do without it. Apparently, then, the Moore calendar would suffer from the same lack of rational correlation between weeks and months that plagues the Gregorian calendar. Also, Moore did not take on the problem of intercalation to account for the fractional number of sols in the year.

William G. Rohrer’s paper "Systemy Czasu Zlawiska Zwiazane z Czasem na Marsie" appeared in the Polish publication Posepy Astronautyki. He miscalculates the length of the Martian year, arriving at the figure of 667.620 sols, while the length of the Martian tropical solar year is 668.5921 sols. It is also worth noting that Rohrer has a record four different lengths of calendar years, which is rather cumbersome. His intercalation formula is:

Rohrer's 19 months, which are designated by Greek letters, are of a uniform length of 35 sols, and since he retains the seven-sol week, as a consequence, his calendar is of the fixed-week type. However, the fact that 19 is a prime number obviously means that his calendar year cannot be divided by any other number while simultaneously dividing into an integral number of months. Since 19 x 35 = 665, the residual sols, either 2, 3, 4, or 5, occur outside of the seven-sol week. I am not fluent in Polish, so I am only guessing that these residual days occur at the end of the year, in similar fashion to the Coptic calendar.

The Rohrer calendar year begins on the southern hemisphere’s vernal equinox, that is to say, the northern hemisphere’s autumnal equinox. His calculation of the length of the Martian seasons also contains some errors. The values he gives are:

Rohrer provides no epoch for his calendar.

Makoto Nagatomo, of the Institute of Space and Astronautical Sciences in Japan, happened to independently develop the same approach as Henry's, that of Martian months spanning the same arcs of the Martian orbit as their Terran counterparts with respect to Earth's orbit. Nagatomo's treatment of the subject also went to about the same depth as Henry's, since his ideas on Martian timekeeping appeared only as an ancillary discussion in his short story, "High-Speed Mars Railway", which was published in the Winter 1979 issue of Uchu Jidai. As with the Henry calendar, Nagatomo did not design his to be perpetual, nor did he include in his story and reference dates to correlate his calendar with the Gregorian calendar, nor did he entertain any thoughts on intercalation.

At this point, I decided to devise my own "stretched Gregorian" calendar. My results seem to indicate that both the Henry and Nagatomo calendars are out of phase by about a month. Henry's longest month is June and his shortest is December, while Nagatomo's July is longer that his June by only a sol and both his November and December contain 48 sols. According to my results, aphelion should occur in late May, making it the longest month, and perihelion should happen in late November, causing it to be the shortest month.

James Lovelock and Michael Allaby contributed some thoughts on Martian timekeeping in their 1984 book The Greening of Mars. They divided the sol into the conventional 24-hour, 60-minute, and 60-second system, just as Levitt did. Although Lovelock and Allaby noted the correct length of the Martian solar day as 24 hours 39 minutes 35 seconds, and intended that their Martian calendar be based on the Martian solar year, they made the mistake of having 687 sols in their calendar when this is in fact the number of terrestrial solar days in a Martian solar year. A popularly written mixture of fact and speculation told in the format of a narrative by a fictional citizen of Mars of the twenty-third century, The Greening of Mars informs the reader:

Mars has a year of 687 days. To be more precise, it is 686.9804 days, which means we have 'leap years' every so often to keep the calendar straight. Our 'leap years' are not like those of Earth, though, which is why I use the expression in quotation marks. On Mars leap years come every fifty-one years, and we lose a day.

It was obvious to Lovelock and Allaby that the cycles of Phobos and Deimos are entirely unsuitable as the bases for units of time. But, whereas others chose to adopt some artificial chronometric unit to divide up the Martian year into anywhere from ten to 24 parts, there are no months at all in the Lovelock-Allaby calendar:

We do not count months. On Earth these are based, clumsily, on the orbit of the Moon. Indeed, we have two tiny moons that look about the size Venus looks when seen from Earth. A division of the year into months would force us to choose one in preference to the other, and that would cause endless wrangling among the Phobos and Deimos factions that would spring up instantly. Even then it would not be easy. Phobos orbits Mars three times each day, and Deimos takes rather more than a day to make a single orbit. Martian months would be rather different from terran months! Perhaps we could use both and try to devise a double-month system. I cannot begin to imagine what that would be like.

Recognizing the sociological necessity of the seven-day week, Lovelock and Allaby adopted this unit of time which has no astronomical analogue either on Earth or Mars. Their calendar thus consists of sols, weeks, and years. They retained the same names of the sols of the week that are used on Earth, and the weeks themselves were numbered from the beginning to the end of the year. As their fictional character explains:

My date of birth, for the record, was 3.68.06. That is to say, I was born on the third day (which we call Tuesday, as I said) of the sixty-eighth week of the sixth year of the century. We omit the number of the century, but I was born in the year 106.

Lovelock and Allaby chose to begin their Martian chronology with the establishment of the first human outpost on Mars. They were unclear as to whether they intended the anniversary of this event to be New Year's Day on their calendar, or if this would merely define the first year of the calendar while New Year's Day would be fixed by some other occurrence such as the vernal equinox. In any case, since the beginning of their chronology is defined by an event which has yet to come about, their calendar cannot be referenced to the Gregorian calendar. The table shows the Lovelock-Allaby calendar corrected for the 668.6-sol year.

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